In designing a filter circuit, appropriately combining resistors, capacitors, coils, operational amplifiers configure a passive filter or an active filter. Some specific examples are some single-tuned circuits using resistors, capacitors and coils, and further, a Butterworth, Chebyshev, Bessel or an elliptic function filters combining an operational amplifier with the elements. These filters have such a characteristic of which the phase of the output signal changes with the frequency of it. The reason is that the ratio between the imaginary number component and the real number component of the impedance of these filters changes with frequency. In the signal processing, when the phase change with frequency is at least linear in characteristic, the group delay characteristic is flat. Thus, we can remove the distortion of the output with respect to the input signal waveform. With the Bessel filter, for example, limiting the frequency flattens the group delay characteristic as far as possible.
A single tuned circuit that is one of the conventional filter units is shown in FIG. 30. This single tuned circuit comprises a resistor 130 having a resistance value of 10 k.OMEGA., a coil 50 having an inductance value of 0.01 H, and a capacitor 52 having a capacitance value of 10 pF connected in series, and a signal source 140 having a phase of zero degree and an amplitude of unity connected across the series circuit. The output signal's amplitude and phase characteristic with respect to the input signal of this single tuned circuit is shown in FIGS. 31 to 33. FIG. 31 shows the lowpass filter characteristic obtained at a terminal 13, FIG. 32 shows the band rejection filter characteristic obtained at a terminal 14, and FIG. 33 shows the bandpass filter characteristic obtained between the terminals 14 and 15. FIGS. 31 and 32 show that, in spite of the cut off frequency of about 500 kHz, the phase begins to change already at 10 kHz in a signal-pass frequency range. FIG. 33 shows that the phase changes sharply at both side of central frequency of signal-pass frequency range.
In the case where the chrominance.signal is taken out of the composite video signal of a TV signal using these conventional bandpass filters, unevenness of group delay develops in the frequency about the carrier frequency. Therefore, a distortion occurs in the waveform after demodulation, sometimes inconveniently making an adverse effect in doing faithful color reproduction. For removing the high harmonics from the demodulated chrominance signal, a lowpass filter is used, so that a comparatively large phase delay is developed for the signal. To correct the time delay due to the phase delay, inserting a delay line in a luminance signal processing circuit having no time delay is necessary.
The FDNR (frequency dependent negative converter) has been proposed as one of the impedance converts (also called GIC), which comprises a combination of two operational amplifiers and five elements in which two elements are made up capacitors and the remaining elements are resistors.
This FDNR has the characteristic that the phase characteristic of it remains unchanged with frequency but the resistance value of it changes with frequency. Nevertheless, the resistance characteristic of FDNR is negative and is limited to the square of the frequency. Also, since replacing the value of each component element with another value is needed for changing the resistance value, the field in which the FDNR is applicable was limited.
Further, when noises are removed from the pulse signal using these conventional lowpass filters, the large phase change sometimes causes a considerable difference between the phase of the input pulse and that of the pulse output. Especially, there happened a serious trouble in a circuit requiring synchronous processing.